Density of states in a two-dimensional chiral metal with vacancies

TL;DR

This paper investigates how vacancies in a two-dimensional chiral metal alter its electronic properties, revealing divergence in the density of states and the emergence of zero modes, with implications for understanding disorder effects.

Contribution

It introduces a novel analysis of vacancies as a form of chiral disorder, showing their unique impact on the density of states and critical properties at zero energy.

Findings

Density of states diverges as E^{-1} |ln E|^{-3/2} near zero energy

Correlation length scales as sqrt{|ln E|} at low energies

Vacancies induce zero modes and open a gap, which is smeared by interference effects

Abstract

We study quantum interference effects in a two-dimensional chiral metal (bipartite lattice) with vacancies. We demonstrate that randomly distributed vacancies constitute a peculiar type of chiral disorder leading to strong modifications of critical properties at zero energy as compared to conventional chiral metals. In particular, the average density of states diverges as $\rho \propto E^{-1} |\ln E|^{-3/2}$ and the correlation length $L_c \propto \sqrt{|\ln E|}$ in the limit $E \to 0$. When the average density of vacancies is different in the two sublattices, a finite concentration of zero modes emerges and a gap in the quasiclassical density of states opens around zero energy. Interference effects smear this gap resulting in exponentially small tails at low energies.